I'm not sure how Satan used a snake to speak to Eve. Animals were placed under Adam's dominion; and since angels are ministering spirits sent forth to minister for those who shall be heirs of salvation, perhaps different animals came under the jurisdiction of different ministering spirits, responding to Adam's dominion over the animals, under God. And since the snake was more subtle than any other creature, perhaps it was the more likely candidate to be used by Satan on this occassion.
But Adam could have rebuked it. God questioned Eve and Adam before explaining the curse which they would henceforward suffer because of their disobedience, but God never questioned the snake - and yet He pronounced to the snake the curse which it too would henceforward come under. Animals don't have moral responsibility - and yet the snake species still incurred a curse.
All of creation suffered in the fall. Plant and animal life became subject to death; even the very characteristics of some fauna and flora may have changed.
Perhaps the act of tempting Eve was part-and-parcel of Satan's fall - rather than his fall being something that had already taken place in previous aeons. And perhaps when a third of the angels fell with Satan that day, those animals which may have been under their jurisdiction may have at that time incurred the character changes that seem to reflect the fallen characteristics of those spirits.
As early as pre-flood times, some animals were already being called unclean while others were clean. Compare your feelings about a sheep and a pig, or a dove and a vulture. Satan is called Beelzebub, the lord of the flies. The Bible does talk about angelic creatures in heaven, so perhaps some demons even look like the animals which may once have been their jurisdiction before the fall. Jesus said, "Behold I give unto you power over snakes and scorpions and over all the power of the enemy".
Even some plant life changed its characteristics after the fall: thorns and thistles and perhaps strangling vines and poisons may have come into existence at that time.
All of physical creation groans, waiting for the redemption, the manifestation of the sons of God, when corruption shall be swallowed up in victorious resurrection. Perhaps the planet itself and the heavens shall be made anew.
We are waiting for the Day when our own bodies, and flora, and fauna, and the earth and heavens itself, shall be made new at the coming of our Lord and Savior.
In the meantime, we can exercize our Christ-given authority over snakes and scorpions and over all the power of the enemy. Jesus bound the strongman, and spoiled his goods - and anyone who believes in Jesus will do as He did and greater works shall he do because He returned to the Father.